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United States Patent |
5,729,015
|
Tong
|
March 17, 1998
|
Position control system for scanning probe microscope
Abstract
A position control system for a scanning probe microscope which performs
calculations so that the natural resonant frequency of a piezoelectric
element may be as flat as possible, and then controls the scanning voltage
of the piezoelectric element. The scanning signal from outside a position
control circuit is inputted to an integral compensator via a comparator.
The output of the integral compensator is supplied from an adder to the
piezoelectric element via a high-voltage amplifier and also to a reference
model section. The output of the piezoelectric element, together with the
output of the reference model section, is supplied to a comparator and at
the same time, is fed back to the comparator via a displacement sensor.
Furthermore, the comparator inputs a correcting voltage Va to an adder via
an adaptive mechanism section. The scanning voltage added at the adder is
amplified at the high-voltage amplifier, which supplies the amplified
voltage to the piezoelectric element as a control voltage Vp.
Inventors:
|
Tong; Yi (Hachioji, JP)
|
Assignee:
|
Olympus Optical Co., Ltd. (Tokyo, JP)
|
Appl. No.:
|
591092 |
Filed:
|
January 25, 1996 |
Foreign Application Priority Data
| Jan 30, 1995[JP] | 7-012472 |
| Mar 27, 1995[JP] | 7-067916 |
Current U.S. Class: |
250/306; 73/105 |
Intern'l Class: |
H01J 037/00 |
Field of Search: |
250/306,307
73/105
|
References Cited
U.S. Patent Documents
4843293 | Jun., 1989 | Futami | 318/609.
|
5336887 | Aug., 1994 | Yagi et al. | 250/306.
|
5376790 | Dec., 1994 | Linker et al. | 250/306.
|
5381101 | Jan., 1995 | Bloom et al. | 250/306.
|
5469734 | Nov., 1995 | Schuman | 73/105.
|
5481908 | Jan., 1996 | Gamble | 250/306.
|
5496999 | Mar., 1996 | Linker et al. | 250/306.
|
5521390 | May., 1996 | Sato et al. | 250/306.
|
5543614 | Aug., 1996 | Miyamoto et al. | 250/306.
|
Foreign Patent Documents |
63-189911 | Aug., 1988 | JP.
| |
6-229753 | Aug., 1994 | JP.
| |
Primary Examiner: Anderson; Bruce
Attorney, Agent or Firm: Frishauf, Holtz, Goodman, Langer & Chick
Claims
What is claimed is:
1. A scanning probe microscope comprising:
a cantilever having a fixed end portion and a free end portion;
a probe provided at said free end portion of said cantilever;
moving means for holding one of said probe and a specimen, and for moving
relative positions of said probe and said specimen;
scanning signal output means for outputting a scanning signal for scanning
said moving means;
moving amount detecting means for detecting a moving amount of said moving
means based on said scanning signal, and for outputting a movement signal
which corresponds to said detected moving amount;
a feedback control system including first correction signal generating
means for generating a first correction signal for canceling a deviation
between said movement signal and said scanning signal; and
a follow-up control system including: (i) a reference model unit for
outputting a theoretical movement signal of said moving means based on
said first correction signal; and (ii) a second correction signal
generating means for generating a second correction signal for canceling a
deviation between said movement signal and said theoretical movement
signal, and for outputting said second correction signal to said moving
means.
2. The scanning probe microscope according to claim 1, wherein said
reference model unit comprises a low-pass filter represented by a preset
transmission function, according to which said theoretical movement signal
is calculated.
3. The scanning probe microscope according to claim 1, wherein said second
correction signal generating means comprises:
a comparator for calculating a deviation between said movement signal and
said theoretical movement signal;
a proportional differential compensator for outputting said second
correction signal based on an output signal from said comparator; and
an adder for adding said second correction signal to said first correction
signal.
4. The scanning probe microscope according to claim 1, wherein said first
correction signal output from said first correction signal generating
means comprises a signal for moving one of said probe and said specimen on
an XY plane which substantially coincides with a surface of said specimen.
5. The scanning probe microscope according to claim 1, wherein:
said first correction signal output from said first correction signal
generating means comprises a signal for moving one of said probe and said
specimen on an XY plane which substantially coincides with a surface of
said specimen;
said reference model unit comprises a low-pass filter represented by a
preset transmission function, according to which said theoretical movement
signal is calculated; and
said second correction signal generating means comprises:
a comparator for calculating a deviation between said movement signal and
said theoretical movement signal;
a proportional differential compensator for outputting said second
correction signal based on an output signal from said comparator; and
an adder for adding said second correction signal to said first correction
signal.
6. A scanning probe microscope comprising:
a cantilever having a fixed end portion and a free end portion;
a probe provided at said free end portion of said cantilever;
moving means for holding one of said probe and a specimen, and for moving
relative positions of said probe and said specimen;
moving amount detecting means for detecting a moving amount of said moving
means, and for outputting a movement signal which corresponds to said
detected moving amount;
a feedback control system including: (i) displacement detection means for
detecting a displacement amount of said cantilever based on a change in an
interaction between said probe and said specimen, and for outputting a
displacement signal which corresponds to said detected displacement amount
of said cantilever; and (ii) control signal outputting means for
outputting a control signal for controlling a position of said moving
means based on said displacement signal output by said displacement
detection means; and
a follow-up control system including: (i) a reference model unit for
outputting a theoretical movement signal which corresponds to a
theoretical movement amount of said moving means based on said control
signal; and (ii) a correction signal generating means for generating a
correction signal for canceling a deviation between said movement signal
and said theoretical movement signal, and for outputting said correction
signal to said moving means.
7. The scanning probe microscope according to claim 6, wherein said
reference model unit comprises a low-pass filter represented by a preset
transmission function, according to which said theoretical movement signal
is calculated.
8. The scanning probe microscope according to claim 6, wherein said
correction signal generating means comprises:
a comparator for calculating a deviation between said movement signal and
said theoretical movement signal;
a proportional differential compensator for outputting said correction
signal based on an output signal from said comparator; and
an adder for adding said correction signal to said control signal.
9. The scanning probe microscope according to claim 6, wherein said control
signal servo-controls said moving means such that a displacement of said
cantilever which is caused by said interaction between said probe and said
specimen is maintained constant.
10. The scanning probe microscope according to claim 6, further comprising:
an XY directional scanning unit for outputting a signal for scanning said
moving means in X and Y directions; and
a display unit for displaying a three-dimensional measurement image of said
specimen, responsive to an input of said movement signal and said XY
scanning signal.
11. The scanning probe microscope according to claim 6, further comprising:
an XY directional scanning unit for outputting a signal for scanning said
moving means in X and Y directions; and
a display unit for displaying a three-dimensional measurement image of said
specimen, responsive to an input of said movement signal and said XY
scanning signal;
wherein said control signal servo-controls said moving means such that a
displacement of said cantilever which is caused by said interaction
between said probe and said specimen is maintained constant;
wherein said reference model unit comprises a low-pass filter represented
by a preset transmission function, according to which said theoretical
movement signal is calculated; and
wherein said correction signal generating means comprises:
a comparator for calculating a deviation between said movement signal and
said theoretical movement signal;
a proportional differential compensator for outputting said correction
signal based on an output signal from said comparator; and
an adder for adding said correction signal to said control signal.
12. A scanning probe microscope comprising:
a cantilever having a fixed end portion and a free end portion;
a probe provided at said free end portion of said cantilever;
moving means for holding one of said probe and a specimen, and for moving
relative positions of said probe and said specimen;
displacement detection means for detecting a displacement amount of said
cantilever based on a change in an interaction between said probe and said
specimen, and for outputting a displacement signal which corresponds to
said detected displacement amount,
a feedback control system including control signal outputting means for
outputting a control signal for controlling a position of said moving
means based on said displacement signal output by said displacement
detection means; and
a follow-up control system including: (i) a reference model unit for
outputting a theoretical movement signal which corresponds to a
theoretical movement amount of said moving means based on said control
signal; and (ii) a correction signal generating means for generating a
correction signal for canceling a deviation between said displacement
signal and said theoretical movement signal, and for outputting said
correction signal to said moving means.
13. The scanning probe microscope according to claim 12, wherein said
reference model unit comprises a low-pass filter represented by a preset
transmission function, according to which said theoretical movement signal
is calculated.
14. The scanning probe microscope according to claim 12, wherein said
correction signal generating means includes:
a comparator for calculating a deviation between said displacement signal
and said theoretical movement signal;
a proportional differential compensator for outputting said correction
signal based on an output signal from said comparator; and
an adder for adding said correction signal to said control signal.
15. The scanning probe microscope according to claim 12, wherein said
control signal servo-controls said moving means such that a displacement
of said cantilever which is caused by said interaction between said probe
and said specimen is maintained constant.
16. The scanning probe microscope according to claim 12, further
comprising:
an XY directional scanning unit for outputting a signal for scanning said
moving means in X and Y directions; and
display means for displaying a three-dimensional measurement image of said
specimen, responsive to an input of said movement signal and said XY
scanning signal.
17. The scanning probe microscope according to claim 12, further
comprising:
an XY directional scanning unit for outputting a signal for scanning said
moving means in X and Y directions; and
a display unit for displaying a three-dimensional measurement image of said
specimen, responsive to an input of said movement signal and said XY
scanning signal;
wherein said control signal servo-controls said moving means such that a
displacement of said cantilever which is caused by said interaction
between said probe and said specimen is maintained constant;
wherein said reference model unit comprises a low-pass filter represented
by a preset transmission function, according to which said theoretical
movement signal is calculated; and
wherein said correction signal generating means includes:
a comparator for calculating a deviation between said displacement signal
and said theoretical movement signal;
a proportional differential compensator for outputting said correction
signal based on an output signal from said comparator; and
an adder for adding said correction signal to said control signal.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to a position control system for a scanning probe
microscope, and more particularly to a position control system for a
scanning probe microscope using a reference model of a piezoelectric
element that presents a flat characteristic at the natural resonant
frequency .omega..sub.p of the piezoelectric element.
2. Description of the Related Art
Three-dimensional scanning mechanisms using piezoelectric elements have
been widely used to move a minute movement stage with a resolution on the
order of nanometers. For scanning probe microscopes (SPM) requiring atomic
resolution, such as a scanning tunneling microscope (STM) that forms an
image by tracing the surface of the specimen in atomic-level dimensions by
means of tunnel current or such as an atomic force microscope (AFM), the
scanning mechanisms have been popularized widely as a mechanism for
driving a stage that determines the x, y, and z directions of the specimen
or the probe.
In general, the scanning probe microscopes are three-dimensional measuring
instruments that cause the probe to approach the specimen, sense a
physical quantity acting between them, cause the probe to trace (scan) the
unevenness of the specimen's surface on the basis of the physical
quantity, determine the differences in properties of the specimen's
surface on the order of atomic size.
The aforementioned AFM is considered to be one of such scanning probe
microscopes. In the AFM, while the movement of the cantilever being
displaced by the interactive force acting between the atoms at the tip of
the probe and the specimen is electrically or optically being sensed and
determined, the specimen or the probe is scanned in the X and Y directions
and the positional relationship between the probe section of the
cantilever with the specimen's surface is changed relatively, thereby
obtaining information about the unevenness of the specimen on the order of
atomic size three-dimensionally.
Although the AFM has been used as an apparatus for viewing the surface of a
specimen with an ultrahigh resolution, it has recently come into use as an
instrument for measuring the line width, the step height, etc. in a
semiconductor or a liquid crystal.
With scanning probe microscopes, to prevent the degradation of the picture
quality due to the resonant characteristic of the piezoelectric element,
the development of high-speed, high-accuracy position control techniques
has been demanded. Therefore, a technique for increasing the accuracy of
the position control system for servo and scanning on the order of micron
or nanometer has been in great demand.
FIG. 1 shows an example of the configuration of a conventional scanning
probe microscope.
In FIG. 1, a cylindrical piezoelectric element 2 outputs xp and yp of the
actual displacement to an XY position control circuit 6. An X, Y position
command section 4 outputs scanning signals x, y to the XY position control
circuit 6. The XY position control circuit 6 then outputs an X control
signal (a driving voltage for the piezoelectric element in the X
direction) Vx* and a Y control signal (a driving voltage for the
piezoelectric element in the Y direction) Vy* to the piezoelectric element
2.
Although the control signals Vx* *, Vy are signals that drive the
piezoelectric element 2 on the basis of the scanning signals x, y, they
are used as signals for correcting the displacements when the actual
displacements xp, yp of the piezoelectric element 2 do not coincide with
the scanning signals x, y. Namely, they are used as feedback control
signals.
The scanning signal x, y and the actual displacements xp, yp are inputted
to the XY position control circuit 6, which compares them. The correction
signal obtained on the basis of the comparison is applied in voltage form
from the XY position control circuit 6 to the piezoelectric element,
thereby causing the actual displacements xp, yp of the piezoelectric
element 2 to coincide with the scanning signals x*, y*.
Inside the piezoelectric element 2, a mirror 10 for measuring displacements
in the X and Y directions is provided at the top of the piezoelectric
element 2. Almost in the central portion, a lens 12 for gathering rays of
laser light is provided. The bottom end of the piezoelectric element 2 is
secured to a unit containing an X displacement sensor 14 and a Y
displacement sensor 16. The X displacement sensor 14 and Y displacement
sensor 16 are sensors for sensing the two-dimensional movement of the
piezoelectric element 2 and output the actual displacement xp, yp to the
XY position control circuit 6. They have been described in detail in the
scanning system disclosed in, for example, Jpn. Pat. Appln. KOKAI
Publication No. 6-229753, so that their explanation will not be given
here.
On the top of the piezoelectric element 2, the specimen carrier 18 for
holding a specimen 20 is positioned. A probe displacement sensing section
24 has a cantilever 22 at its tip portion and senses the displacement of
the cantilever 22 optically and electrically. The probe displacement
sensing section 24 outputs a displacement signal Sz to the Z displacement
servo control section 8.
The Z displacement control section 8 performs feedback control so that the
displacement of the cantilever 22 may remain constant, and outputs a Z
control signal (a driving voltage for the piezoelectric element in the Z
direction) Vz* that expands and contracts the piezoelectric element 2 in
the Z direction, that is, information on the unevenness of the
displacement, to an SPM image display unit 26. The SPM image display unit
26 stores the measurement data based on the transferred Vz* and forms an
image. In FIG 1, X indicates the X direction, Y the Y direction, and Z the
Z direction.
FIG. 2 is a block diagram of the Z displacement servo control section 8 of
the scanning probe microscope of FIG. 1 and its peripheral section.
In FIG. 2, the difference between the reference signal Z* and the actual
displacement signal Sz of the piezoelectric element 34 sensed at the
displacement sensor 40 is obtained at the comparator 38. Thereafter, the
difference is integrated at the integral compensator 30, which produces a
voltage Vz to be applied to the piezoelectric element 34.
FIG. 3 is a block diagram of the configuration of the X scanning feedback
control system of the conventional piezoelectric element 2 shown in FIG.
1. Only the X scanning feedback system is shown in FIG. 3. The same is
true for the Y scanning feedback control system.
In FIG. 3, a scanning signal x* and the actual displacement x.sub.p are
inputted to a comparator 28, the output of which is supplied to an
integral compensator 30. The output of the integral compensator 30 is
supplied to a piezoelectric element 34 via a high-voltage amplifier 32.
The output of the piezoelectric element 34 is the actual displacement,
which is supplied to the comparator 28 via a displacement sensor 36.
Here, in the Z displacement servo control system of FIG. 2, it is assumed
that the gain Kh of the high-voltage amplifier 32 of FIG. 3 is Kh=1.
Namely, the gain Kh is omitted.
Hereinafter, the integral gain of the integral compensator 30 is indicated
by K.sub.ci in both the XY directions and the Z direction. The integral
gain K.sub.ci is one of the parameters that determine the response speed
of the piezoelectric element 34. For example, as the integral gain
K.sub.ci is increased, the response speed of the piezoelectric element 34
gets faster accordingly.
In the X scanning feedback control system of FIG. 3, the function written
at the piezoelectric element 34 is the transfer function of the
piezoelectric element 34.
Ks in FIG. 3 indicates the gain of the displacement sensor 36.
As seen from an example of the frequency characteristic actually measured
in the X direction of the cylindrical piezoelectric element shown in FIG.
4, however, the vibration of the piezoelectric element peaked at 1900 Hz.
In this case, the damping coefficient .xi..sub.p (=0.0169) is much less
than 0.7, the ideal value with no vibration, from which it is found that
the cylindrical piezoelectric element is a mechanical vibration system
with a poor damping characteristic.
FIG. 5A is a Bode diagram of the Z-axis displacement of a conventional
piezoelectric element, the integrator gain, and the applied voltage
frequency characteristic. As shown in FIG. 5A, a peak appears at a
resonant frequency of about 6400 Hz (indicated by f0) in the piezoelectric
element 34, wherein fi is used to evaluate the control band of the control
system.
Therefore, it is understood that the resonant frequency differs with the
movement direction and the characteristic of the piezoelectric element 34,
but the frequency characteristic is almost the same in the examples shown
in both FIG. 4, FIGS. 5A and 5B.
It is known, however, that when the peak value of the gain characteristic
of the resultant closed loop at the resonance point has exceeded 0 dB, the
control system becomes unstable. This is a problem common to both the
piezoelectric element 34 of FIG. 4 and that of FIGS. 5A and 5B.
Here, "unstable" means that as the response speed of the piezoelectric
element is increased, the position control system is more liable to permit
the piezoelectric element to vibrate. Therefore, the control system has
performed control by causing the integral compensator to adjust the
integral gain K.sub.ci so that the peak value of the resultant closed loop
gain characteristic at the resonance point may not exceed 0 dB.
The control will be explained in detail below.
First, the Z displacement servo control system will be explained.
As shown_in FIG. 5B, to minimize the influence in the vicinity of the
first-order resonant frequency of the Z-axis piezoelectric element, the
gain characteristic of the integrator is dropped at a frequency much lower
than the resonance point of the piezoelectric element 34. Namely, the
integral gain K.sub.ci is set small. This makes it possible to suppress
the peak of the resultant closed loop gain characteristic at the resonance
point to 0 dB or less.
In other words, in the conventional Z displacement servo control system of
FIG. 2, as the integral gain K.sub.ci increases, the resultant closed loop
gain characteristic shifts to the right as shown in FIG. 5B, raising the
resonance peak of the piezoelectric element 34, with the result that the
control system becomes unstable. Therefore, in practical use, the integral
gain K.sub.ci must be very small.
Hereinafter, using FIGS. 6 and FIGS. 7, a case will be explained where the
Z displacement servo control system is unstable when the integral gain
K.sub.ci of the integral compensator 30 is increased, or when the scanning
speed is increased.
FIG. 6A shows the step response characteristic for an integral gain
K.sub.ci =250 in the prior art. With the integral gain, it took about 25
msec for the rising of the curve to be stable. When the integral gain
K.sub.ci has exceeded 500, the step response gets faster (about 15 msec)
as shown in FIG. 6B, but the control system becomes unstable and
eventually oscillates and cannot be controlled.
FIGS. 7A to 7C are response characteristic diagrams for the Z-direction
displacement servo control system of a conventional scanning probe
microscope using the aforementioned piezoelectric element. The cross
section of the specimen is rectangular. The unevenness of the specimen's
surface has a level difference of about 500 nm. In FIGS. 7A to 7C, the
actual shapes are shown by broken lines and the follow-up characteristic
is shown by solid lines.
FIG. 7A is a characteristic diagram to help explain the case where the
piezoelectric element is following the level differences of the unevenness
of the specimen's surface in the Z direction in scanning the specimen in
the X direction at a constant scanning speed. It can be seen from the FIG.
7A that the follow-up characteristic is poor and the rising does not
follow the step and makes a gentle curve. To make the response faster, the
gain of the integrator must be set greater. As shown in FIG. 7B, however,
it can be seen that as the gain of the integrator becomes larger, the
response gets faster, but is oscillating. Furthermore, when the
X-direction scanning speed is doubled, the piezoelectric element fails to
follow the unevenness of the specimen's surface as shown in FIG. 7C.
As described above, because the Z-direction servo produces a poor response
to the unevenness cross section of the specimen shown in FIGS. 7A to 7C,
the positioning accuracy cannot be raised. Thus, in the case of a specimen
having large and sharp bumps, measurement errors occur in the Z direction,
so that high-speed two-dimensional scanning cannot be effected and
consequently high-speed measurement cannot be carried out. In the case of
a specimen with a large level difference in the unevenness, the probe hits
the specimen's surface during scanning because the response of the servo
is slow, resulting in the danger of causing damage to the probe or the
surface of the specimen.
The replacement of the specimen carrier or the specimen causes the
resonating point of the piezoelectric element to shift toward lower
frequencies as a result of an increase in the weight of the specimen
carrier or the specimen, so that the control gain must be lowered further.
This causes the problem that the parameters of the control system have to
be adjusted each time the specimen carrier or the specimen is replaced.
Explained next will be the X scanning feedback system shown in FIGS. 3 and
4.
In the scanning control system in the conventional scanning probe
microscope having the XY displacement sensors, the response signal of FIG.
9B follows the scanning signal at a scanning speed of 1 Hz shown in FIG.
9A. As the scanning speed becomes as fast as 10 Hz, however, the
piezoelectric element fails to follow the scanning signal at the turning
point of time in scanning as shown in FIGS. 8A and 8B. In addition, since
follow-up errors are proportional to the turning speed, the faster the
scanning speed, the greater the follow-up errors.
As described above, the maximum scanning speed of the SPM is also limited
by the XY direction vibration characteristic of the piezoelectric element.
To suppress the vibrating characteristic of the piezoelectric element, for
example, Jpn. Pat. Appln. KOKAI Publication No. 63-189911 has disclosed
control means in which an acceleration sensor is used to supply the sense
signal to an acceleration first-order delay circuit and the delayed signal
is added to the applying voltage instruction. The system, however,
requires an acceleration sensor and a processing circuit, so that the
inevitable result is that the system gets complicated and larger.
Furthermore, as described earlier, with the scanning probe microscope, to
prevent the deterioration of the picture quality, the development of
high-accuracy, high-speed position control techniques has been demanded.
As the XY scanning speed gets faster, the response in the Z direction must
be made much faster.
The basic idea of realizing high-speed scanning and response in the
scanning probe microscope comes from making the resonant frequency of the
Z-axis minute movement mechanism piezoelectric element as high as possible
and the amplitude during resonance as small as possible. Namely, the
stiffness of the piezoelectric element is made as high as possible. The
improvement of the position control accuracy of the piezoelectric element
is considered to be achieved by the higher stiffness of the piezoelectric
element and the higher gain of the control system.
Since all of the materials of the mechanism have a finite mass and a finite
stiffness, however, the increase of the natural frequency has a
limitation.
SUMMARY OF THE INVENTION
The object of the present invention is to provide a position control system
for a scanning probe microscope which not only makes the control system
stabilize and respond faster, but also prevents the probe from hitting a
specimen's surface during scanning and causing damage to the probe or the
specimen's surface, which eliminates the need to adjust the parameters of
the control system each time the specimen carrier or the specimen is
replaced, and which does not make the system more complicated or larger.
It is an object of the present invention to provide a scanning probe
microscope comprising: a cantilever having a fixed end portion and a free
end portion; a probe provided at the free end portion of the cantilever;
moving means for holding either the probe or a specimen and moving the
relative positions of them; control signal output means for outputting a
control signal for performing position control of the moving means; actual
movement sensing means for sensing the actual movement of the moving means
on the basis of the control signal output means; theoretical value output
means for outputting the theoretical movement of the moving means on the
basis of the control signal output means; correcting signal output means
for outputting a correcting signal for canceling the deviation of the
actual movement from the theoretical movement; and correction control
signal generating means for generating, on the basis of the control signal
and the correcting signal, a correction control signal to be supplied to
the moving means.
It is another object of the present invention to provide a scanning probe
microscope comprising: a cantilever having a fixed end portion and a free
end portion; a probe provided at the free end portion of the cantilever;
moving means for holding either the probe or a specimen and moving the
relative positions of them; control signal output means for outputting a
control signal for performing position control of the moving means; probe
displacement sensing means for sensing the probe displacement; theoretical
value output means for outputting the theoretical movement of Z position
of the moving means on the basis of the control signal output means;
correcting signal output means for outputting a correcting signal for
canceling the deviation of the probe displacement from the theoretical
movement; and correction control signal generating means for generating,
on the basis of the control signal and the correcting signal, a correction
control signal to be supplied to the moving means.
With the invention, in the XY scanning control system of a scanning probe
microscope using a piezoelectric actuator, a reference model section
(theoretical value output means) with a transfer function Ga(s) like a
convectional scanning control system having a flat frequency
characteristic at the natural resonant frequency .omega..sub.p of the
piezoelectric element, is caused to move the vibrating pole point of the
transfer function Gp(s) of the piezoelectric actuator to suppress the
resonance peak of the piezoelectric actuator according to the flat
characteristic, thereby making the control system respond faster and
stabilize better. This makes it possible to stabilize the mechanical
vibration system with a poor damping characteristic. Furthermore, this
makes it possible to set the gain of the position control loop higher,
which not only makes the response of the position control system faster,
but also raises the accuracy. In this way, the problem that the scanning
speed cannot be raised in the position control system using an integral
compensator can be solved, enabling the piezoelectric element to move in
the XY two-dimensional directions at high speeds.
Furthermore, with the scanning probe microscope of the present invention,
the displacement Sz of the probe of the cantilever is sensed from the
displacement sensing section or tunnel current sensing section of the
cantilever. The displacement Sz is compared with a previously set
reference value. The deviation .DELTA.Z is integrated at the integrator,
which produces an applying voltage Vz*. The applying voltage Vz* is passed
through a specific low-pass filter, which produces the output Zm of the
reference model of the piezoelectric element. The deviation .DELTA.S
obtained from the output Zm of the reference model of the piezoelectric
element and the displacement Zk in the Z direction of the piezoelectric
element supplied from the piezoelectric element Z-direction displacement
sensing section is input to the proportion differential control section.
The proportion differential control section calculates .DELTA.V. On the
basis of the calculation result, the applying voltage Vz to the
piezoelectric element is controlled in such a manner that the following
equations (1) and (2) are fulfilled so that the actual displacement of the
piezoelectric element may follow the output of the reference model:
Vz=Vz*-.DELTA.V (1)
##EQU1##
where K.sub.ap and K.sub.ad indicate the proportional differential gains.
As described above, with the scanning probe microscope of the present
invention, by sensing the displacement of the piezoelectric element,
comparing the sensed displacement with the output of the reference model
that does not resonate, and positively controlling the deviation, the
voltage applied to the piezoelectric element is adjusted so as to suppress
the mechanical resonance peak of the piezoelectric element. As a result,
the control band is expanded and the gain of the control loop can be set
high, which makes it possible to speed up the response of the Z-direction
displacement servo control system.
Furthermore, the Z-direction control accuracy is increased, and it is also
possible to sense minute changes in the information on the specimen's
surface stably at high speeds without slowing the scanning speed in the XY
directions of the piezoelectric element. In the case of a specimen with
great and sharp irregularities in the surface, there is no possibility
that serious damage will be caused to the probe or the specimen's surface.
Even when a change in the weight of the specimen carrier or the specimen
causes the resonating point of the piezoelectric element to change, it is
possible to sense minute changes in the information on the specimen's
surface stably at high speeds.
Additional objects and advantages of the invention will be set forth in the
description which follows, and in part will be obvious from the
description, or may be learned by practice of the invention. The objects
and advantages of the invention may be realized and obtained by means of
the instrumentalities and combinations particularly pointed out in the
appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part
of the specification, illustrate presently preferred embodiments of the
invention and, together with the general description given above and the
detailed description of the preferred embodiment given below, serve to
explain the principles the invention.
FIG. 1 shows an example of the configuration of a conventional scanning
probe microscope;
FIG. 2 is a block diagram of the Z-displacement servo control section in
the scanning probe microscope of FIG. 1 and its peripheral circuitry;
FIG. 3 is a block diagram of the XY scanning feedback control system in the
conventional piezoelectric actuator of FIG. 1;
FIG. 4 is a frequency characteristic diagram in the X direction of a
cylindrical piezoelectric element;
FIG. 5A is a Bode diagram showing the Z-axis displacement of a conventional
piezoelectric element, the gain of an integrator, with the applying
voltage frequency characteristic, and FIG. 5B is a Bode diagram showing
the frequency characteristic of the closed loop into which the individual
components in FIG. 5A are combined;
FIG. 6A is a step response characteristic diagram in the prior art for an
integral gain of K.sub.ci =250 and FIG. 6B is a step response
characteristic diagram for an integral gain of K.sub.ci =500 or more;
FIGS. 7A to 7C are diagrams to help explain the follow-up characteristic
for the unevenness of a specimen's surface of the Z-direction displacement
servo control system in the conventional scanning probe microscope;
FIGS. 8A and 8B are timing charts for the response characteristic of a
10-Hz triangle scanning signal in the scanning control system of a
conventional scanning probe microscope having XY displacement sensors,
FIG. 8A being a waveform diagram of the scanning signal, and FIG. 8B being
a waveform diagram of the response signal;
FIGS. 9A and 9B are timing charts for the response characteristic of a 1-Hz
triangle scanning signal in the scanning control system of a conventional
scanning probe microscope having XY displacement sensors, FIG. 9A being a
waveform diagram of the scanning signal, and FIG. 9B being a waveform
diagram of the response signal;
FIG. 10 is a block diagram of the position control system in a scanning
probe microscope according to the present invention;
FIG. 11 is a diagram of a root locus showing the change of the pole of the
closed loop for an integral gain of K.sub.ci in a general control system;
FIG. 12 is a diagram of a root locus of a closed loop drawn with K.sub.ap
=100 and K.sub.ad =1 as parameters in the present invention;
FIG. 13 is a diagram in which the X-direction frequency characteristic
(broken lines) of a cylindrical piezoelectric element is compared with the
frequency characteristic (solid lines) of the reference model section;
FIGS. 14A and 14B are timing charts for the response characteristic of a
10-Hz triangle scanning signal in the scanning control system in the
scanning probe microscope of FIG. 10, FIG. 14A being a waveform diagram of
the scanning signal, and FIG. 14B being a waveform diagram of the response
signal;
FIGS. 15A and 15B are timing charts for the response characteristic of a
50-Hz triangle scanning signal in the scanning control system in the
scanning probe microscope of FIG. 10, FIG. 15A being a waveform diagram of
the scanning signal, and FIG. 15B being a waveform diagram of the response
signal;
FIG. 16 is a step response characteristic diagram of the control system in
the embodiment;
FIG. 17 is a block diagram of the Z displacement servo control system in a
scanning probe microscope according to a second embodiment of the present
invention;
FIGS. 18A and 18B are diagrams for the follow-up characteristic for the
unevenness of the specimen's surface of the Z-direction displacement servo
control system in the scanning probe microscope of the second embodiment;
FIG. 19 is a block diagram of the position control system in a reverse
scanning probe microscope according to a modification of the second
embodiment of the present invention; and
FIG. 20 is a block diagram of the position control system in a scanning
probe microscope according to a third embodiment of the present invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Hereinafter, referring to the accompanying drawings, embodiments of the
present invention will be explained.
FIG. 10 is a block diagram of the position control system in a scanning
probe microscope according to the present invention. The basic
configuration of the scanning probe microscope is the same as that of FIG.
1, and although only the X scanning feedback control system will be
described herein below, the same is true for the Y scanning feedback
control system.
In FIG. 10, the position control system is includes of an adaptive
mechanism section and a follow-up control section based on an adaptive
model. In FIG. 10 the follow-up control section is enclosed by broken
lines.
A scanning signal x* supplied from outside a position control circuit is
inputted to an integral compensator 52 via a comparator 50. The output
(scanning voltage Vc*) of the integral compensator 52 is supplied from an
adder 54 to a piezoelectric element 58 via a high-voltage amplifier 56 and
also to a reference model section 60 having a transfer function of the
displacement of the piezoelectric element 58 free from the influence of
disturbances such as vibration.
The displacement XP of the piezoelectric element 58 A2 is sensed by the
displacement sensor 64 which has a gain of Ks. The displacement Xp sensed
by the displacement sensor 64 is supplied together with the output of A3
the reference model section 60 to a comparator 62 and also fed back to the
comparator 50. The comparator 62 inputs a correcting voltage Va to an
adder 54 via an adaptive mechanism section 66.
The integrator 52 inputs a scanning voltage Vc* to the follow-up control
section, in which the reference model section 60 calculates a displacement
Xm as a reference model, that is, a displacement free from vibration or
disturbance.
The adaptive mechanism section 66 suitably amplifies the deviation of
position Xm of the reference model section 60 from the actual displacement
x.sub.p of the piezoelectric element 58 and calculates a correcting
voltage Va. The correcting voltage Va is added to the scanning voltage
Vc*.
Then, the adaptive mechanism section 66 generates a control input
(correcting voltage) Va so that the displacement x.sub.p of the
piezoelectric element 58 may follow the output Xm of the reference model
section 60. If the transfer function Gp(s) of the piezoelectric element 58
coincides with the transfer function Gm(s) of the reference model section
60 completely, it will follow that Va=0, meaning that the control system
is equivalent to the conventional control system as shown in FIG. 3.
Specifically, the scanning signal x is compared with the displacement
x.sub.p of the piezoelectric element 58 sensed by the displacement sensor
64'. An error in the comparison result is computed at the integral
compensator 52, which generates a scanning voltage Vc* applied to the
piezoelectric element 58. The scanning voltage Vc* is inputted to the
reference model section 60. The output Xm from the reference model section
60 is compared with the actual displacement x.sub.p of the piezoelectric
element 58 at the comparator 62. The error .epsilon. in the comparison
result from the comparator 62 is corrected by a PD compensator
(proportional differential compensator), the adaptive mechanism section
66, which generates a correcting voltage Va. In this way, the correcting
voltage Va is added to the scanning voltage at the adder 54. Thereafter,
the scanning voltage is amplified by the high-voltage amplifier 56 and
supplied as a control voltage Vp to the piezoelectric element 58.
Here, the difference between position control using a conventional usual
integral compensator and position control according to the present
invention will be described.
In the case of position control using a conventional usual integral
compensator as shown in FIG. 3,
##EQU2##
where Kh is the gain of the high-voltage amplifier 56, and Ks is the gain
of the displacement sensor 64.
The gain Kh of the high-voltage amplifier 56 may be Kh=11, which has no
serious effect on the invention.
FIG. 11 shows a root locus indicating the change of the pole of the closed
loop for an integral gain of K.sub.ci of the control system for the
piezoelectric element having the frequency characteristic of FIG. 4. The
scanning feedback control system of FIG. 2 is used as the closed loop. In
FIG. 11, the symbol x represents a pole. Because the damping coefficient
of the piezoelectric element (piezoelectric actuator) 58 is .xi..sub.p <1,
a set of conjugate roots are:
##EQU3##
As shown in FIG. 11, as the gain K.sub.ci increases, the root locus
starting from vibrating poles P.sub.2 P.sub.3 goes from the half plane on
the left side of the imaginary axis into that on the right side of the
imaginary axis as shown in the figure. Since control on the half plane on
the left side of the imaginary axis is known to be stable control, if the
control system performs control on the half plane on the right side of the
imaginary axis, the system will be unstable as shown in the step response
characteristic of FIG. 6B. Thus, in practical use, K.sub.ci must be less
than the limit gain K.sub.lim =500 in the case of FIG. 11.
With the position control system in a general scanning probe microscope,
the gain of the closed loop cannot be made greater in the case of the
vibration system with a poor damping characteristic as described earlier,
so that the response of the closed loop gets worse. Consequently, as the
scanning speed gets faster, the piezoelectric element cannot follow the
scanning signal at its turning point. As the weight of the specimen
carrier and specimen increases, the resonating point of the piezoelectric
element shifts toward low frequencies, so that the control gain has to be
lowered further. This makes the follow-up characteristic much worse.
The suppressing effect of position control according to the present
invention is as follows.
It is assumed that in the control system of FIG. 10, Gc(s) is a transfer
function for the integral compensator 52, Gp(s) is a transfer function for
the piezoelectric element 58, Gm(s) is a transfer function for the
reference model section 60, and Ga(s) is a transfer function for the
adaptive mechanism section 66. The respective transfer functions for the
integral compensator 52, piezoelectric element 58, reference model section
60, and adaptive mechanism section 66 are expressed as the following
equations (5) to (8):
##EQU4##
where K.sub.ci is the integral gain of the integral compensator 52,
K.sub.ap and K.sub.ad are the proportional and differential gains of the
adaptive mechanism section 66, A.sub.p, .xi..sub.p, and .omega..sub.p are
parameters of the piezoelectric element 58, and Am, .xi..sub.m, and
.omega..sub.m are parameters of the reference model section 60.
A proportional differential compensator according to equation (5) is used
in the adaptive mechanism section 66. A second-order low-pass filter
according to equation (8) is used in the reference model section 60 of the
piezoelectric element.
As seen from FIG. 10, the position control system of the present invention
is obtained by adding only the reference model section 60 and proportional
differential compensator (adaptive mechanism section 66) to a conventional
general position control system. If it were not for the reference model
section 60 and adaptive mechanism section 66, the position control system
of the invention would be essentially the same as the conventional
feedback control system as shown in FIG. 3.
The transfer function of the open loop of the control system in the
embodiment is expressed as the following equation (9):
##EQU5##
Since mechanical constants .xi..sub.p and .omega..sub.p and gains K.sub.ap
and K.sub.ad are used in equation (9) representing the characteristic of
the control system, the operation of adaptive follow-up model control can
be analyzed using the above equation.
In equation (9), if K.sub.ap =0 and K.sub.ad =0, the same equation as
equation (3) will be given. Even with a mechanical system with a poor
damping characteristic, the damping characteristic of the system can be
improved by adding a control system as shown in the embodiment and setting
the proportional and differential gains K.sub.ap and K.sub.ad of the
adaptive mechanical section at suitable values.
As described above, when a control system as shown in the embodiment is
added, the transfer function of the open loop changes from equation (3) to
equation (9). By determining the pole of the transfer function, the
damping and response characteristics of the system can be estimated.
Now, as an example, a piezoelectric element having the frequency
characteristic as shown in FIG. 4 will be considered. In FIG. 4, it is
assumed that a piezoelectric element has a damping coefficient .xi..sub.p
=0.016, a natural resonant frequency .omega..sub.p of 11938 ›rad/s!, and
parameter A.sub.p =0.04. Thus, this piezoelectric element is a very poor
damping system. When a control system of the embodiment is applied to the
piezoelectric element, the gains K.sub.ap and K.sub.ad of the adaptive
mechanism can be determined by examining a root locus according to
equation (13).
FIG. 12 shows a root locus of the closed loop drawn using parameters
K.sub.ap =100 and K.sub.ap =1. From the figure, it is understood that by
setting the gains K.sub.ap and K.sub.ad of the adaptive mechanism section
66 at suitable values, the vibrating point of the piezoelectric element
moves from point A to point B and point A' to point B' as shown by the
solid lines. As a result, the damping coefficient .xi. of the system is
improved from 0.016 to 0.707. As shown in FIG. 12, the limit K.sub.lim of
the integral gain Ki increases from 500 in the conventional system as
shown in FIG. 11 to 4000.
Specifically, as compared with the distance from point A (A') to point C
(C') on the root locus curve in the allowable range of the differential
gain of the conventional control system, the allowable range of the
integral gain in the control method of the embodiment is expanded from
point B (B') to point C (C') on the root locus curve.
Furthermore, with the configuration, the vibrating pole point of the
transfer function Gp(s) of the piezoelectric element 58 is moved to
suppress the resonance peak of the cylindrical piezoelectric element as
shown by broken lines in FIG. 13 on the basis of the reference model
section having a flat characteristic as shown by solid lines in the
figure, which thereby enables the control system to respond faster and
stabilize better.
FIG. 16 is a step response diagram for the control system in the
embodiment. As compared with the response characteristic diagram for the
conventional control system of FIGS. 6A and 6B, the rise-time is obviously
shortened remarkably.
For XY triangle wave scanning, equation (5) may be as follows:
##EQU6##
The fact that equation (5') is valid in the invention is apparent to those
skilled in the art.
FIGS. 14A and 14B show the response characteristic of a 10-Hz triangle wave
scanning signal in the control system in the embodiment. It is understood
that the piezoelectric element follows the scanning signal completely, as
compared with the response characteristic diagrams of the conventional
control system shown in FIGS. 9A and 9B.
FIGS. 15A and 15B show the response characteristic of a 50-Hz triangle wave
scanning signal in the control system in the embodiment. As seen from the
figure, the piezoelectric element provides a good follow-up characteristic
by scanning even with a 50-Hz triangle wave. This means that high-speed
scanning is possible.
Because the position control system in the conventional scanning probe
microscope without a control system of the invention has a very low
damping coefficient of .XI..sub.p =0.016, the increase of the control gain
can cause the control system to vibrate. The faster the response of the
position control system (the larger the gain K.sub.ci), the larger the
amplitude of the vibration, which has an adverse effect on measurement, so
that high-speed scanning is impossible. The application of the
above-described control system improves the damping coefficient remarkably
and makes the control gain larger, with the result that the vibration can
be suppressed.
As described above, when the damping coefficient .xi..sub.p and natural
resonant frequency .omega..sub.p of the piezoelectric element are known,
the gains K.sub.ap and K.sub.ad of the reference model section and
adaptive mechanism section can be set suitably, thereby producing a great
effect in suppressing resonant vibration.
With the position control system in a scanning probe microscope according
to the invention, the reference model section is composed of an ordinary
low-pass filter (e.g., a second-order low-pass filter) and the adaptive
mechanism section can be constructed very simply so as to perform
proportional and differential control. In addition, the position control
system uses no special sensor. Therefore, just by adding small software,
the invention can be applied to a conventional position control system
that performs integral control by a simple feedback using a microcomputer.
As described above, the application of the aforementioned control system to
the XY scanning position control system in the scanning probe microscope
produces the following effects:
(i) Suppressing resonant vibration of the piezoelectric element, thereby
enabling the control system to operate faster and stabilize better
(ii) Solving the problem that a scanning probe microscope cannot speed up
the scanning speed in a two-dimensional direction as a result of the
degradation of the follow-up characteristic at the turning point of the
scanning line in conventional feedback control.
The aforementioned control system of the invention is used for XY scanning
control of a scanning probe microscope and may, of course, be used for
Z-direction servo control. Hereinafter, as a second embodiment of the
present invention, a Z displacement servo control system will be
explained.
FIG. 17 is a block diagram of the Z displacement servo control system in a
scanning probe microscope according to a second embodiment of the present
invention.
In FIG. 17, the scanning probe microscope comprises a specimen carrier 72
that supports a specimen 70 to be measured, a cylindrical piezoelectric
element 74 that supports and moves the specimen carrier 72, a cantilever
76 having a probe at its free end, a probe displacement sensing section
78, a cantilever Z-direction displacement control section 80, an XY signal
scanning section 82, a model follow-up control section 84, a piezoelectric
element displacement sensor 86 for sensing the Z-direction displacement of
the piezoelectric element, a piezoelectric element Z-direction
displacement sensing section 88, and an SPM (image) display unit 90.
The probe displacement sensing section 78 optically and electrically senses
the displacement of the probe of the cantilever 76 caused by the
interaction between the probe of the cantilever 76 and the specimen 70 and
outputs a displacement signal Sz to the Z-direction displacement control
section 80. The Z-direction displacement control section 80 performs
feedback control so as to keep constant the distance between the surface
of the specimen 70 and the probe's tip of the cantilever 76, and has a
displacement sensing function and an integral function.
Specifically, the probe displacement sensing section 78 supplies the
displacement Sz of the probe to the Z-direction displacement control
section 80, which compares the displacement Sz with the previously set
reference value, causes an integrator (not shown) to integrate the
resulting deviation .DELTA.Z, generates the applying voltage Vz*, and
outputs the voltage to the model follow-up control section 84.
Vz*=K.sub.ci .intg..DELTA.Zdt (10)
where K.sub.ci is the integral gain of the integral compensation.
On the other hand, in the piezoelectric element Z-direction displacement
sensing section 88, the Z-direction piezoelectric element displacement
sensor 86 placed on the specimen carrier 72 senses the actual displacement
Zk of the piezoelectric element 74. The sensed displacement signal Zk is
inputted to the model follow-up control section 84 and image display unit
90.
The XY scanning signals Vx and Vy outputted from the XY signal scanning
section 82 are applied to the piezoelectric element 74, which is scanned
in two-dimensional directions. The XY scanning signals Vx and Vy at this
time, together with the displacement signal Zk from the piezoelectric
element Z-direction displacement sensing section 88, is transferred to the
image display unit 90.
The model follow-up control section 84 comprises a low-pass filter 92, a
proportional differential control section 94, and comparators 96 and 98.
The order of the low-pass filter is the same as that of the first-order
resonance peak in the Z direction of the piezoelectric element 74. The
low-pass filter 92 may be composed of an analog filter or a digital
filter.
The piezoelectric element displacement sensor 86 may be composed of, for
example, an optical sensor or an electrostatic sensor, which is capable of
directly sensing the displacement in the Z direction of the piezoelectric
element 74.
The individual parts of the scanning probe microscope shown in FIG. 17
correspond to the individual parts of the scanning probe microscope of
FIG. 10. Specifically, the integral compensator 52, adder 54, comparator
62, displacement sensor 64, reference model section 60, and adaptive
mechanism section 66 in FIG. 10 correspond to the cantilever Z-direction
displacement control section 80, comparator 98, comparator 96, probe
displacement sensing section 78, piezoelectric element Z-direction
displacement sensing section 88, low-pass filter 92, and proportional
differential control section 94. This configuration provides the response
characteristic shown in FIG. 16.
With such a configuration, receiving the voltage instruction Vz* from the
cantilever Z-direction displacement control section 80, the model
follow-up control section 84 passes the voltage instruction through the
low-pass filter 92, which generates a displacement Zm as a reference model
of the piezoelectric element 74. The displacement Zm is a displacement
that is not affected by vibration or disturbance. Then, the comparator 96
compares the output Zm of the reference model with the actual displacement
Zk of the piezoelectric element 74 and outputs a deviation .DELTA.S
(=Zm-Zk). The deviation .DELTA.S is input to the proportion differential
control section 84. The section 84 calculates .DELTA.V and Vz as indicated
by the following equations (11) and (12):
##EQU7##
Vz=Vz*-.DELTA.V (12)
where K.sub.ap and K.sub.ad are the proportional and differential gains in
the proportional differential control section.
The deviation is corrected at the proportional differential control section
94, which generates a corrected voltage .DELTA.V. The corrected voltage
.DELTA.V is added to the applying voltage Vz* at the comparator 98. This
enables control to be performed so that the displacement Zk of the
piezoelectric element 74 may follow the reference model output Zm.
In the vicinity of the resonating point, the applying voltage to the
piezoelectric element 74 is particularly reduced, thereby suppressing the
effect of the mechanical resonance peak of the piezoelectric element 74.
If the response of the piezoelectric element 74 completely coincides with
the output of the reference model, the corrected voltage .DELTA.V=0 will
be given, with the result that control system will be equivalent to the
conventional control system.
FIGS. 18A and 18B show the follow-up characteristic for the unevenness of a
specimen's surface of the Z-direction displacement servo control system in
the scanning probe microscope according to the second embodiment. For
comparison with the conventional control system, the control conditions,
that is, the bumps in the specimen and the scanning speed, are set equal
to those in FIGS. 7A and 7C. In FIGS. 18A and 18B, the cross section of
the actual specimen is shown by broken lines, and the follow-up
characteristic is shown by solid lines.
As described above, with the second embodiment, as shown in FIG. 18A, it is
understood that the piezoelectric element almost follows the unevenness of
the specimen's surface in the Z direction during scanning at a constant
scanning speed in the X direction. As compared with the response
characteristic diagram of FIG. 7A in the prior art, the follow-up
characteristic of the piezoelectric element for the unevenness of the
specimen's surface is obviously improved.
As shown in 18B, even though the scanning speed in the X direction is
doubled, the follow-up characteristic of the piezoelectric element is
good. As compared with the response characteristic in the prior art of
FIG. 7C, the response characteristic shown in FIGS. 18A and 18B has a
remarkably short rise-time, with the result that high-speed scanning is
possible.
As described above, by sensing the displacement of the piezoelectric
element, comparing the displacement with the output of the reference model
that does not resonate, and positively controlling the deviation, the
voltage applied to the piezoelectric element is adjusted, thereby
suppressing the mechanical resonance peak of the piezoelectric element
sufficiently. As a result, the control band is expanded, which enables the
gain of the control loop to be set high, causing the Z-direction
displacement servo control system to respond faster.
Furthermore, it is possible to make the control accuracy in the Z direction
higher and sense minute changes in the information on the specimen's
surface stably at high speeds without slowing the scanning speed in the XY
directions of the piezoelectric element. Even in the case of large and
sharp bumps in the specimen's surface, there is no possibility that
serious damage will be caused to the probe or the specimen's surface
during scanning.
Furthermore, even if the resonating point of the piezoelectric element
changes as a result of the change of the specimen carrier or specimen, it
is possible to sense minute changes in the information on the specimen's
surface stably at high speeds without changing the control gain.
Similar analysis of the Z-direction control system using the root locus can
make the control gain larger as confirmed in FIG. 12. Therefore, the
control band is expanded, allowing the gain of the control loop to be set
higher, so that the response of the Z direction displacement servo control
system can be made faster.
While in the second embodiment, the probe scanning microscope has the
specimen carrier and specimen placed on the piezoelectric element, the
invention is not limited to this. For instance, a cantilever scanning
probe microscope as shown in FIG. 19 may be used.
Specifically, a cantilever 76' having a probe and a displacement sensing
plate 100 are provided on the bottom end of the piezoelectric element 74'.
Below the probe of the cantilever 76', the specimen carrier 72 is located.
The specimen 70 is put on the specimen carrier 72. The piezoelectric
element displacement sensor 86 provided near and above the plate 100
senses the displacement of the piezoelectric element 74'. The remaining
configuration is the same as that of FIG. 17, so explanation of it will
not be given.
With such a configuration, because the weight of the specimen carrier and
specimen does not change, the resonating point of the piezoelectric
element will not change either. Consequently, the control band will not
change, making it easier to set the gain of the control loop higher, with
the result that the response of the Z-direction displacement servo control
system can be made faster.
Hereinafter, a third embodiment of the present invention will be explained.
FIG. 20 is a block diagram of the position control system in a scanning
probe microscope according to a third embodiment of the present invention.
With the scanning probe microscope, the displacement of the piezoelectric
element is sensed indirectly by sensing the displacement of the
cantilever.
In FIG. 20, the scanning probe microscope comprises a specimen carrier 72
that supports a specimen 70, a piezoelectric element 74 that supports and
moves the specimen carrier 72, a cantilever 76 having a probe at its free
end, a probe displacement sensing section 78 that optically senses the
displacement of the cantilever 76 due to the interaction between the probe
of the cantilever 76 and the specimen 70, a cantilever Z-direction
displacement control section 80, an XY signal scanning section 82, a model
follow-up control section 84, and an SPM (image) display unit 90.
The probe displacement sensing section 78 senses the displacement of the
probe of the cantilever 76 optically and electrically, outputs a
displacement signal Sz to the cantilever Z-direction displacement control
section 80 and to the image display unit 90 and a comparator 96 in the
model follow-up control section 84.
The cantilever Z-direction displacement control section 80 performs
feedback so as to keep constant the distance between the surface of the
specimen 70 and the tip of the probe of the cantilever 76, and compares
the displacement Sz of the probe sensed at the probe displacement sensing
section 78 with the previously set reference value Z*. After the
comparison, it causes an integrator (not shown) to integrate the deviation
.DELTA.Z, generates an applying voltage Vz*, and outputs it to the model
follow-up control section 84 (refer to the above equation (10)).
The model follow-up control section 84 comprises a low-pass filter 92,
comparators 96 and 98, a proportional differential control section 94.
The cantilever Z-direction displacement control section 80 passes the
voltage instruction Vz* through the low-pass filter 92, which generates a
displacement Zm as a reference model of the piezoelectric element 74.
Then, the comparator 96 compares the output Zm of the reference model
(low-pass filter 92) with the actual displacement Sz of the cantilever
sensed at the probe displacement sensing section 78. The deviation is
calculated at the proportional differential control section 94 using the
above equations (11) and (12). Specifically, the deviation is corrected at
the proportional differential control section 94, which generates a
corrected voltage .DELTA.V. Then, the corrected voltage .DELTA.V is added
to the applying voltage Vz at the comparator 98.
This enables the piezoelectric element 74 to be controlled so that the
reference model output Zm may follow the actual displacement Sz of the
cantilever 76. In the vicinity of the resonating point, the applying
voltage to the piezoelectric element 74 is reduced, thereby suppressing
the mechanical peak of the piezoelectric element 74.
In the third embodiment, the mechanical resonant frequency of the
cantilever 76 must be twice as high as the mechanical resonant frequency
of the piezoelectric element 74.
As described above, by sensing the displacement of the piezoelectric
element through the sensing of the displacement of the cantilever,
comparing the displacement of the piezoelectric element with the output of
the reference model that does not resonate, and positively controlling the
deviation, the voltage applied to the piezoelectric element is adjusted,
thereby suppressing the mechanical resonance peak of the piezoelectric
element sufficiently. As a result, the control band is expanded, which
enables the gain of the control loop to be set high, causing the
Z-direction displacement servo control system to respond faster.
Furthermore, it is possible to make the control accuracy in the Z direction
higher and sense minute changes in the information on the specimen's
surface stably at high speeds without slowing the scanning 10 speed in the
XY directions of the piezoelectric element. Even in the case of large and
sharp bumps in the specimen's surface, there is no possibility that
serious damage will be caused to the probe or the specimen's surface
during scanning.
While in the embodiments, the atomic force microscope is used, the present
invention may, of course, be applied to a scanning tunneling microscope
(STM).
Furthermore, while in the embodiments, the invention is applied to a
scanning probe microscope, it may, of course, be applied to the
positioning unit in an exposure device in manufacturing semiconductors.
Additionally, the reference model can be constructed very easily. For
instance, it may be composed of a simple low-pass filter. Therefore, by
just adding a little software or hardware, the present invention can be
applied easily to a position scanning control system that performs
conventional control, so that it is very practical.
The embodiments described above pertain to X scanning feedback control, Y
scanning feedback control and Z-direction displacement servo control,
respectively. The present invention, however is not limited to the
described embodiments. Rather, X scanning feedback control, Y scanning
feedback control and Z-direction displacement servo control may be
combined, constituting an XYZ control system.
Additional advantages and modifications will readily occur to those skilled
in the art. Therefore, the invention in its broader aspects is not limited
to the specific details, and representative devices shown and described
herein. Accordingly, various modifications may be made without departing
from the spirit or scope of the general inventive concept as defined by
the appended claims and their equivalents.
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